where \(V\)  is the volume in 3D or the area in 2D, occupied by polaritons.
The transition to the continuous system is accurate if the differences between eigenfrequencies are much less than \(T\)  [1]}.
Note that the delta function with prefactor unity in the right-hand side of Eq. (REF ) suggests that at \({\bf k}={\bf 0}\)  there is only one state.
Such a separation of the state \({\bf k}={\bf 0}\)  is a standard step in the description of continuous systems [2]}.
Below we consider the quadratic dispersion, \(\omega _{\bf k} = \omega _{\bf 0} + \alpha {\bf k}^2\) .
This dispersion is characteristic for polaritons of the lower branch in the vicinity of \({\bf k} = {\bf 0}\)  and the most frequent case in the experimental realizations of BEC.
